470 TRANSACTIONS OF THE AMERICAN INSTITUTE. 



observations, the first being in 1784. He finds an increaise of 

 about three seconds between the minimum observed by him and 

 those noted in 1S59 by Masterraan. These periodical changes 

 have been the sul)ject of much speculation among astronomers^ 

 but, while nothing is known with certainty, regarding the cause 

 of light in our own sun, it seems useless to attempt to explain the 

 cause of the variable illumination of a self-luminous star or sun 

 situated at an immense distance from the solar system. It is, 

 however, important to record, with all possible accuracy, frequent 

 observations of celestial chansfes, because they may hereafter 

 materially assist in the solution of problems now altogether 

 beyond our grasp. 



E. B. Ellicott, Esq., of Boston, read a paper on the 



Mutual Action of Elements op Electric Currents. 



The law of Ampere — that commonly recognized as expressing 

 the action of two independent elements (or infinitesimal portions 

 of electric currents) — was based on an assumption, and on four 

 cases of equilibrium experimentally determined. The assumption 

 of Ampere was that the direction of the action was constant, inde- 

 pendent of the relative directions of the elements, and that the 

 quantity of intensity of the force raised with the direction of the 

 elements. The new assumption was the reverse of this — to wit : 

 that the intensity of the resultant is independent of the direction 

 of the elements ; but that the direction of the resultant varies 

 with the direction of the elements. The latter view more closely 

 corresponds to the doctrine, now generally admitted as established, 

 of the conservation of the phj^sical forces. It is also, in form, 

 more analagous to the law expressive of the natural action of 

 material masses under the influence of gravity. 



In the case of gravity the action w'as proportioned directl}-- to 

 the product of the masses, and inversely to the square of their 

 distance. In the case of electrical, the current's direction of the 

 elements is to be taken into consideration; and the resulting force 

 may be expressed as the product of the quotients of each element, 

 (considered bolh as to strength of current and length and direc- 

 tion of element) divided hy their distance (also considered both 

 as to length and direction); the consideration of direction involves 

 the application of the newly developed principles of the mathe- 

 matical science of quatemoris. 



The law above mentioned having assumed all the ordinary spe- 



